One of the most impressive, innovative advances in online fundraising over the p
ID: 3245759 • Letter: O
Question
One of the most impressive, innovative advances in online fundraising over the past decade is the rise of crowd-funding websites. While features differ from site to site, crowd-funding sites are websites that allow you to set up an online fundraising campaign based around a fundraising page, and accept money directly from that page using the website's own credit card processor. A certain crowd-funding website reported that 134 of 353 technology crowd-funding projects were successfully launched in the past year and 342 of 880 film and video crowd-funding projects were successfully launched in the past year.
Complete parts (a) through (c) below
a. Is there evidence of a significant difference in the proportion of technology crowd-funding projects and film and video crowd-funding projects that were successful? (Use = 0.1.)
State the null and alternative hypotheses, where 1 is the population proportion of successful technology crowd-funding projects and 2 is the population proportion of successful film and video crowd-funding projects.
A. H0: 1 = 2; H1: 1 > 2
B. H0: 1 2; H1: 1 > 2
C. H0: 1 2; H1: 1 < 2
D. H0: 1 = 2; H1: 1 < 2
E. H0: 1 = 2; H1: 1 2
F. H0: 21 2; H1: 1 = 2
Determine the value of the test statistic.
ZSTAT = ____? (Type an integer or a decimal. Round to two decimal places as needed.)
Determine the critical value(s) for this test of hypothesis.
The critical value(s) is (are) ____. (Round to two decimal places as needed. Use a comma to separate answers as needed.)
State the conclusion.
(Reject, Do not reject) the null hypothesis. There is (sufficient, insufficient) evidence to support the claim that there is a significant difference in the proportion of successful technology crowd-funding projects and successful film and video crowd-funding projects.
b. Determine the p-value in (a) and interpret its meaning.
The probability of obtaining a difference in proportions that gives rise to a test statistic (less than or equal to, contained in the interval between, more extreme or equal to, greater than or equal to) the (negative test statistic, test statistic, test statistic and its negative) is equal to the p-value of ____? if there is no difference between the population proportions of successful technology crowd-funding projects and successful film and video crowd-funding projects. (Type an integer or a decimal. Round to three decimal places as needed.)
c. Construct and interpret a 90% confidence interval estimate for the difference between the proportion of technology crowd-funding projects and film and video crowd-funding projects that are successful. The researchers performing this study can be (95%, 10%, 99%, 90%, 5%, 1%) confident that the difference in the population proportion of successful technology crowd-funding projects and successful film and video crowd-funding projects is (greater than the upper bound of, less than the lower bound of, equal to the midpoint of, contained in) the interval from ____? To ____?. (Type integers or decimals. Round to four decimal places as needed.)
Explanation / Answer
1 is the population proportion of successful technology crowd-funding projects and
2 is the population proportion of successful film and video crowd-funding projects.
X1 = 134 , n1 = 353 , ,X2 = 342 n2 = 880
p1^ = 134/353 = 0.3796
p2^ = 342/880 = 0.3886
Z-stat = (p1^-p2^) /sqrt(p1q1/n1 + p2q2/n2)
(0.3795 - 0.3886)/sqrt(0.3795 *(1-0.3795 )/353 + 0.3886*(1-0.3886)/880))
=-0.29727
= 0.1 , z-critical = 1.645
since |TS| < 1.645
Do not reject) the null hypothesis. There is (insufficient) evidence to support the claim that there is a significant difference in the proportion of successful technology crowd-funding projects and successful film and video crowd-funding projects.
b)
p-value = 2 P(Z < -0.29727) = 2*0.3831= 0.7662
more extreme or equal to, test statistic and its negative
c)90%
z-critical = 1.645
(p1^ - p2^) = 0.3795 - 0.3886) = -0.0091
sd (p1^ - p2^) = (sqrt(0.3795 *(1-0.3795 )/353 + 0.3886*(1-0.3886)/880)) =0.030611
hence confidence interval =
( -0.0091 -1.645 *0.030611 , -0.0091 +1.645 *0.030611 )
=(-0.0594550,0.04125509)
The researchers performing this study can be (,90%,) confident that the difference in the population proportion of successful technology crowd-funding projects and successful film and video crowd-funding projects is (contained in) the interval from (-0.0594550,0.04125509)
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.